Ligament break-up simulation through pseudo-potential Lattice Boltzmann Method

The Plateau-Rayleigh instability causes the fragmentation of a liquid ligament into smaller droplets. In this study a numerical study of this phenomenon based on a single relaxation time (SRT) pseudo-potential lattice Boltzmann method (LBM) is proposed. If systematically analysed, this test case allows to design appropriate parameters sets to deal with engineering applications involving the hydrodynamics of a jet. Grid convergence simulations are performed in the limit where the interface thickness is asymptotically smaller than the characteristic size of the ligament. These simulations show a neat asymptotic behaviour, possibly related to the convergence of LBM diffuse-interface physics to sharp interface hydrodynamics

Hydrodynamic behavior of the Pseudo-Potential lattice Boltzmann method for interfacial flows

The lattice Boltzmann method (LBM) is routinely employed in the simulation of complex multiphase flows comprising bulk phases separated by non-ideal interfaces. LBM is intrinsically mesoscale with an hydro-dynamic equivalence popularly set by the Chapman-Enskog analysis, requiring that fields slowly vary in space and time. The latter assumptions become questionable close to interfaces, where the method is also known to be affected by spurious non hydrodynamical contributions. This calls for quantitative hydrodynamical checks. In this paper we analyze the hydrodynamic behaviour of LBM pseudo-potential models for the problem of break-up of a liquid ligament triggered by the Plateau-Rayleigh instability. Simulations are performed at fixed interface thickness, while increasing the ligament radius, i.e. in the "sharp interface" limit. Influence of different LBM collision operators is also assessed. We find that different distributions of spurious currents along the interface may change the outcome of the pseudo-potential model simulations quite sensibly, which suggests that a proper fine-tuning of pseudo-potential models in time-dependent problems is needed before the utilization in concrete applications. Taken all together, we argue that the results of the proposed study provide a valuable insight for engineering pseudo-potential model applications involving the hydrodynamics of liquid jets

Low pH, high salinity: too much for Microbial Fuel Cells?

Twelve single chambered, air-cathode Tubular Microbial Fuel Cells (TMFCs) have been filled up with fruit and vegetable residues. The anodes were realized by means of a carbon fiber brush, while the cathodes were realized through a graphite-based porous ceramic disk with Nafion membranes (117 Dupont). The performances in terms of polarization curves and power production were assessed according to different operating conditions: percentage of solid substrate water dilution, adoption of freshwater and a 35mg/L NaCl water solution and, finally, the effect of an initial potentiostatic growth. All TMFCs operated at low pH (pH$=3.0 \pm 0.5$), as no pH amendment was carried out. Despite the harsh environmental conditions, our TMFCs showed a Power Density (PD) ranging from 20 to 55~mW/m$^2 \cdot$kg$_{\text{waste}}$ and a maximum CD of 20~mA/m$^2 \cdot$kg$_{\text{waste}}$, referred to the cathodic surface. COD removal after a $28-$day period was about $45 \%$. The remarkably low pH values as well as the fouling of Nafion membrane very likely limited TMFC performances. However, a scale-up estimation of our reactors provides interesting values in terms of power production, compared to actual anaerobic digestion plants. These results encourage further studies to characterize the graphite-based porous ceramic cathodes and to optimize the global TMFC performances, as they may provide a valid and sustainable alternative to anaerobic digestion technologies.Comment: 13 pages, 10 Figure

Lattice Boltzmann Models with Mid-Range Interactions \ud \ud

An extension of the standard Shan-Chen model for non ideal-fluids, catering for mid-range, soft-core and hard-core repulsion, is investigated. It is shown that the inclusion of such mid-range interactions does not yield any visible enhancement of the density jump across the dense and light phases. Such an enhancement can however be obtained by tuning the exponents of the effective interaction. The results also indicate that the inclusion of soft-core repulsion can prevent the coalescence of neighborhood bubbles, thereby opening the possibility of tailoring the size of multi-droplet configurations, such as sprays and related phase-separating fluids. \ud \u

Structure and isotropy of lattice pressure tensors for multirange potentials

We systematically analyze the tensorial structure of the lattice pressure tensors for a class of multi-phase lattice Boltzmann models (LBM) with multi-range interactions. Due to lattice discrete effects, we show that the built-in isotropy properties of the lattice interaction forces are not necessarily mirrored in the corresponding lattice pressure tensor. This finding opens a different perspective for constructing forcing schemes, achieving the desired isotropy in the lattice pressure tensors via a suitable choice of multi-range potentials. As an immediate application, the obtained LBM forcing schemes are tested via numerical simulations of non-ideal equilibrium interfaces and are shown to yield weaker and less spatially extended spurious currents with respect to forcing schemes obtained by forcing isotropy requirements only. From a general perspective, the proposed analysis yields an approach for implementing forcing symmetries, never explored so far in the framework of the Shan-Chen method for LBM. We argue this will be beneficial for future studies of non-ideal interfaces.Comment: 14 pages + Appendix, 8 figures; updated to published version: added figures and tex

Lattice Boltzmann simulations on the tumbling to tank-treading transition: effects of membrane viscosity

The tumbling to tank-treading (TB-TT) transition for red blood cells (RBCs) has been widely investigated, with a main focus on the effects of the viscosity ratio $\lambda$ (i.e., the ratio between the viscosities of the fluids inside and outside the membrane) and the shear rate $\dot{\gamma}$ applied to the RBC. However, the membrane viscosity $\mu_m$ plays a major role in a realistic description of RBC's dynamics, and only a few works have systematically focused on its effects on the TB-TT transition. In this work, we provide a parametric investigation on the effect of membrane viscosity $\mu_m$ on the TB-TT transition, for a single RBC. It is found that, at fixed viscosity ratios $\lambda$, larger values of $\mu_m$ lead to an increased range of values of capillary number at which the TB-TT transition occurs. We systematically quantify such an increase by means of mesoscale numerical simulations based on the lattice Boltzmann models

Mesoscale perspective on the Tolman length

We demonstrate that the multi-phase Shan-Chen lattice Boltzmann method (LBM) yields a curvature dependent surface tension $\sigma$ as computed from three-dimensional hydrostatic droplets/bubbles simulations. Such curvature dependence is routinely characterized, at first order, by the so-called {\it Tolman length} $\delta$. LBM allows to precisely compute $\sigma$ at the surface of tension $R_s$ and determine the Tolman length from the coefficient of the first order correction. The corresponding values of $\delta$ display universality for different equations of state, following a power-law scaling near the critical temperature. The Tolman length has been studied so far mainly via computationally demanding molecular dynamics (MD) simulations or by means of density functional theory (DFT) approaches playing a pivotal role in extending Classical Nucleation Theory. The present results open a new hydrodynamic-compliant mesoscale arena, in which the fundamental role of the Tolman length, alongside real-world applications to cavitation phenomena, can be effectively tackled. All the results can be independently reproduced through the "idea.deploy" framework.Comment: 10 pages, 5 figures: extended text and added figure